切比雪夫多项式与 Volterra-Fredholm 第一类积分方程

Mohamed Nasseh Nadir, Adel Jawahdou
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引用次数: 0

摘要

人们研究和讨论了大量求解有问题的 Volterra 积分方程和有问题的 Fredholm 积分方程的方法,但很少有同时求解这两种方程的方法。在本研究中,我们将重点研究如何通过用受扰动的对应方程来数值求解第一类有问题的 Volterra-Fredholm 积分方程。我们采用第一类切比雪夫多项式来求解扰动方程。我们的研究结果表明,这种技术方法优于季霍诺夫的正则化方法。它更简单、更省事,并通过各种实例证明了这种简便性。
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Chebyshev polynomials to Volterra-Fredholm integral equations of the first kind
Numerous methods have been studied and discussed for solving ill-posed Volterra integral equations and ill-posed Fredholm integral equations, but rarely for both simultaneously. In this study, we focus on numerically solving the ill-posed Volterra-Fredholm integral equation of the first kind by replacing it with its perturbed counterpart. We employ Chebyshev polynomials of the first kind to solve the perturbed equation. Our findings suggest that this technical approach is superior to the regularization method of Tikhonov. It is simpler, less cumbersome, and this simplicity is demonstrated through various examples.
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